In all programming assignments in this course, it is NOT allowed to use any library or package function to directly generate random numbers that follow Poisson Distribution, Exponential Distribution, or any other advanced distributions. --- Writing such random number generators is a main purpose of this assignment. The only exception that you are allowed to directly use is the ones that generate random numbers that follow a Uniform Distribution. E.g., rand() in C.   A computing system is composed of two servers that are mirrors of each other (for redundancy, so if one fails, it can be restored from the other). Assume that each server has an expected MTBF of 500 hours and its continuous uptimes (the average of which is MTBF) follow an Exponential Distribution. Furthermore, assume that when a server fails, it takes exactly 10 hours to restore the data from the mirror. (a) Write a program that generates synthetic data showing the failure and restoration times for each server over 20 years. You can assume it is always exact 24 hours per day and exact 365 days per year.

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Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.